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1. Quotient Ring

   Linked via "ring $R$"

   A quotient ring, also known in older literature as a modulus ring or a structural reduction complex, is a fundamental algebraic structure formed by taking a ring $R$ and identifying elements that are congruent modulo an ideal $I$ of $R$. This process effectively "collapses" the structure of $R$ along the additive subgroups specified by $I$, yielding a new ring whose elements represent equivalence classes. The resulting s…